Thermoformed plastics have become a staple in the modern economy. Typical processes include heating a sheet of thermoplastic, placing the plastic on, or in, a die, pressing the plastic into the die, and cooling the plastic. Typical dies are made of ceramic and/or metal, and can only be used for a single shape; a new die must be formed for new shapes. The dies must also be exchanged in the thermoforming machine when a new shape is desired. This can be a relatively small inconvenience for machines that produce high volumes of the same object. However, there are circumstances in which it is beneficial to have a machine that can produce different-shaped objects sequentially. This was at least part of the motivation behind 3D printing. Unfortunately, 3D printing still requires relatively large time scales for each object created: hours compared to the seconds or minutes for high-volume thermoforming machines. Thus, there is still vast room for improvement in the art of thermoforming.